There are quite a few companies that produce a wide range of embedded computers, some one them fast enought to play DVDs. And as long as the board is labelled 'embedded', it is likely to have a TTL interface for LCDs.

In the meantime, I am happy with my 200 MHz Geode which plays mp3s and draws GPS maps

Wow, that is steep! Are these prices for the board or some kind of development kit?

The question of 'power' is somewhat subjective. Do you need a Pentium 4 to drive that watch on your wrist? But if you want to do speech recognition and play DVDs at the same time, then yes - you do need a fast CPU.